Properties of Pure Substances: Steam Tables, Saturation, Wet, Superheated, Dryness Fraction, and Mollier Chart

Introduction to Pure Substances

A pure substance is defined as a material that is homogeneous and has a constant chemical composition throughout. It can exist in different phases (solid, liquid, gas), but its chemical identity remains the same. For example, water (H₂O) is a pure substance, whether it is ice, liquid water, or steam. Mixtures, like air or saltwater, are not pure substances because their composition can vary.

In thermodynamics, pure substances are crucial for understanding energy transfer and phase changes, particularly in power cycles and refrigeration cycles. The properties of pure substances, such as temperature, pressure, specific volume, enthalpy, and entropy, are interdependent. This means if we know any two independent intensive properties, we can determine all other properties of the substance.

Phases of a Pure Substance

A pure substance can exist in three common phases: solid, liquid, and vapor (gas). The transitions between these phases are governed by changes in temperature and pressure.

• Solid Phase: Molecules are in fixed positions, arranged in a regular lattice structure. It has a definite shape and volume.
• Liquid Phase: Molecules are close together but can move around. It has a definite volume but takes the shape of its container.
• Vapor (Gas) Phase: Molecules are far apart and move randomly. It has no definite shape or volume and expands to fill its container.

Phase Change Processes

When a pure substance undergoes a phase change, such as melting (solid to liquid), vaporization (liquid to vapor), or sublimation (solid to vapor), its temperature and pressure often remain constant while heat is added or removed. These processes are fundamental to understanding steam tables and thermodynamic diagrams.

Saturation State

The saturation state refers to the condition where a pure substance exists at the point of phase change. For example, at a given pressure, water boils at a specific temperature. This temperature is called the saturation temperature (T_sat), and the pressure is called the saturation pressure (P_sat).

When a substance is in the saturation state, it can coexist in two phases simultaneously. For water at atmospheric pressure (1 atm or 101.325 kPa), the saturation temperature is 100°C. If heat is added to liquid water at 100°C and 1 atm, it will start to vaporize without changing its temperature until all the liquid has turned into vapor.

Types of Saturation States

• Saturated Liquid: The substance is entirely in the liquid phase, but any further addition of heat at constant pressure will cause vaporization.
• Saturated Vapor: The substance is entirely in the vapor phase, but any further removal of heat at constant pressure will cause condensation.
• Saturated Liquid-Vapor Mixture: The substance exists as a combination of liquid and vapor phases in equilibrium.

Dryness Fraction (x)

The dryness fraction is a property used specifically for saturated liquid-vapor mixtures. It represents the quality or proportion of vapor present in the mixture. It is defined as the ratio of the mass of vapor to the total mass of the mixture.

Mathematically, the dryness fraction 'x' is given by:

x = mg / mtotal

where:

• mg is the mass of the vapor component.
• mtotal is the total mass of the mixture (mtotal = mf + mg, where mf is the mass of the liquid component).

The value of dryness fraction ranges from 0 to 1:

• x = 0 corresponds to saturated liquid (100% liquid).
• x = 1 corresponds to saturated vapor (100% vapor).
• 0 < x < 1 corresponds to a saturated liquid-vapor mixture.

Properties like specific volume (v), enthalpy (h), and entropy (s) for a wet mixture can be calculated using the dryness fraction and the corresponding properties of saturated liquid (denoted by subscript 'f') and saturated vapor (denoted by subscript 'g').

For example, specific enthalpy (h) of a wet mixture:

h = hf + x * hfg

where hfg is the enthalpy of vaporization (latent heat), calculated as hfg = hg - hf.

Wet Steam

Wet steam is a saturated mixture of liquid water and water vapor. It exists at saturation temperature and pressure. The dryness fraction of wet steam is always less than 1 (0 ≤ x < 1). For example, steam at 100°C with a dryness fraction of 0.8 is 80% vapor and 20% liquid by mass.

Saturated Steam Tables

Saturated steam tables are essential resources that list the thermodynamic properties of a pure substance at saturation conditions. They are typically organized based on either saturation temperature or saturation pressure.

A typical saturated steam table (organized by temperature) would include columns for:

• Saturation Temperature (T_sat)
• Saturation Pressure (P_sat)
• Specific volume of saturated liquid (v_f)
• Specific volume of saturated vapor (v_g)
• Specific volume of vaporization (v_fg = v_g - v_f)
• Specific internal energy of saturated liquid (u_f)
• Specific internal energy of saturated vapor (u_g)
• Specific internal energy of vaporization (u_fg = u_g - u_f)
• Specific enthalpy of saturated liquid (h_f)
• Specific enthalpy of saturated vapor (h_g)
• Specific enthalpy of vaporization (h_fg = h_g - h_f)
• Specific entropy of saturated liquid (s_f)
• Specific entropy of saturated vapor (s_g)
• Specific entropy of vaporization (s_fg = s_g - s_f)

These tables allow engineers to find the properties of a substance when it is in a saturated state or a wet mixture, provided the temperature/pressure and dryness fraction are known.

Example: To find the specific volume of steam at 100°C and a dryness fraction of 0.9, you would look up the values for v_f and v_g at 100°C from the saturated steam table. From standard tables, at 100°C: v_f ≈ 0.001043 m³/kg and v_g ≈ 1.673 m³/kg. Then, v = v_f + x * v_fg = v_f + x * (v_g - v_f) v = 0.001043 + 0.9 * (1.673 - 0.001043) v = 0.001043 + 0.9 * 1.671957 v = 0.001043 + 1.5047613 v ≈ 1.5058 m³/kg

Superheated Steam

Superheated steam is steam that has been heated above its saturation temperature at a given pressure. In this state, the substance is entirely in the vapor phase and is not in equilibrium with its liquid phase. Superheated steam does not have a dryness fraction, as it is not a mixture of liquid and vapor.

The properties of superheated steam are found in superheated steam tables, which are organized by pressure and then temperature. For a given pressure, as temperature increases above the saturation temperature, the specific volume, enthalpy, and entropy of the superheated steam increase.

To determine the properties of superheated steam, you typically need two independent intensive properties, such as pressure and temperature. For instance, if you need to find the enthalpy of steam at 1 MPa and 300°C, you would consult the superheated steam tables for 1 MPa and look for the row corresponding to 300°C.

Example: From superheated steam tables, at a pressure of 1 MPa (10 bar) and a temperature of 300°C, the specific enthalpy (h) is approximately 3051.6 kJ/kg, and the specific volume (v) is approximately 0.2581 m³/kg.

If the exact temperature is not listed in the superheated steam tables, interpolation (usually linear) is used to find the required property value.

Compressed Liquid (Subcooled Liquid)

A compressed liquid is a liquid that exists at a temperature below its saturation temperature at a given pressure. In this state, the substance is entirely in the liquid phase. The properties of compressed liquids are less sensitive to pressure changes compared to temperature changes. Therefore, the properties of a compressed liquid are often approximated using the properties of the saturated liquid at the same temperature.

For example, the enthalpy of water at 5 MPa and 100°C is very close to the enthalpy of saturated liquid water at 100°C (h_f at 100°C).

The Mollier Chart (h-s Diagram)

The Mollier chart is a graphical representation of the thermodynamic properties of a pure substance, most commonly steam. It is an enthalpy-entropy (h-s) diagram, where enthalpy (h) is plotted on the vertical axis and entropy (s) is plotted on the horizontal axis.

The Mollier chart is incredibly useful for analyzing thermodynamic cycles, such as the Rankine cycle used in power plants, because it visually depicts the energy transfers (enthalpy changes) during different processes.

Key Features of a Mollier Chart

The Mollier chart typically displays several sets of curves representing different properties:

• Constant Pressure Lines: These lines generally slope downwards and to the right. They are widely spaced at high enthalpies and converge at low enthalpies.
• Constant Temperature Lines: These lines are usually shown in the superheated region and are relatively flat, sloping slightly downwards.
• Constant Dryness Fraction Lines (x): These lines are straight and slope upwards from left to right, originating from the saturated vapor line (x=1). They are only present in the wet region.
• Constant Specific Volume Lines (v): These lines are also present, typically in the superheated region.
• Saturation Curve: This is a dome-shaped curve separating the compressed liquid region (left of the dome) from the superheated vapor region (right of the dome). The peak of the dome is the critical point. The left side of the dome represents saturated liquid (x=0), and the right side represents saturated vapor (x=1).

How to Use the Mollier Chart

The Mollier chart allows for quick determination of thermodynamic states and processes:

1. Locating a State: To find a specific state (e.g., superheated steam at a given pressure and temperature), locate the intersection of the corresponding pressure line and temperature line on the chart.

2. Determining Properties: Once a state is located, you can read its enthalpy (vertical axis) and entropy (horizontal axis). You can also find other properties like temperature, pressure, or dryness fraction by following the relevant curves.

3. Analyzing Processes: Thermodynamic processes can be represented as lines or curves on the chart. For example:

• Isenthalpic process (constant enthalpy): A vertical line.
• Isentropic process (constant entropy): A vertical line.
• Isobaric process (constant pressure): Follow the constant pressure line.
• Isothermal process (constant temperature): Follow the constant temperature line.

The change in enthalpy (Δh) during a process can be directly read as the vertical distance moved on the chart, representing the heat added or work done in certain cycles.

Applications in Engineering

Understanding the properties of pure substances and their representation in steam tables and charts is fundamental for analyzing and designing various thermal systems:

• Power Plants: Analyzing the Rankine cycle for steam turbines, boilers, and condensers.
• Refrigeration Systems: Analyzing vapor-compression cycles using refrigerants.
• Internal Combustion Engines: Understanding the combustion process and exhaust gas properties.
• Turbomachinery: Analyzing the expansion and compression of working fluids.

Key Takeaways for Exams

Ensure you are comfortable with:

1. Identifying pure substances and their phases.
2. Understanding saturation conditions (T_sat, P_sat, phase change).
3. Calculating properties of wet steam using dryness fraction (x).
4. Reading and interpolating values from saturated and superheated steam tables.
5. Interpreting the different lines and regions on a Mollier chart (h-s diagram).
6. Applying these concepts to analyze simple thermodynamic cycles.